Two-dimensional (2D) coordinate stages are used in many stages of very-large-scale-integrated (VLSI) circuit fabrication, to position lithography masks and move wafers to predetermined positions with high degree of reproducibility and accuracy. Typical tools which incorporate 2D-coordinate stages include electron and laser beam pattern generators in mask making, optical steppers in wafer printing and placement inspection tools in mask metrology.
In conventional photolithographic processing of semiconductor wafers, a plurality of masks is used in sequence to define microelectronic structures and features therein. Of course, in order to ensure that the features produced with a first mask are properly aligned to features produced with a second mask during a subsequent process step, it is typically necessary that the two masks be properly aligned relative to each other and that the mask patterns used to define the features be accurately located on each mask. In the past, the mask making industry faced little technical challenge in meeting the alignment and accuracy challenges posed by semiconductor process designers, even as critical photolithographic linewidths decreased by a factor of ten (10). The ability to meet these early challenges was due, at least in part, to high resolution and placement accuracy provided by mask pattern generators and the transition in wafer exposure tools from predominantly 1×optical lithography to 5×reduction optical lithography. However, as critical photolithographic linewidth feature sizes continue to shrink, improved techniques and equipment for meeting more precise alignment and accuracy challenges are required.
During fabrication of integrated circuits, a semiconductor wafer is typically mounted on a 2D-coordinate stage. Typically, the (u,v) position and movement of the stage is monitored by a laser-interferometer. As will be understood by those skilled in the art, the measured (u,v) position of the stage will most often contain a deviation from the actual position of the stage in Cartesian coordinates. This deviation is typically referred to as the stage position measurement error. The Cartesian coordinate system has straight and uniform (x,y) grid lines which are orthogonal and have the same scale. As will be understood by those skilled in the art, the stage position measurement error is the sum of (i) random measurement noise (which can be caused by noise in circuitry, mechanical vibration, and air movement, etc.) and (ii) systematic measurement error (which is a function of the stage position, and can arise from, for example, the non-orthogonality between the x-y mirrors, curvature of the mirrors, etc.). The systematic measurement error is also called stage distortion. Accordingly, a proper calibration of 2D-coordinate stages generally requires the determination of the stage distortion by mapping the measured stage position to its respective position in the Cartesian coordinate grid.
Most stand-alone apparatus that have 2D-coordinate stages for VLSI processing and testing constitute a 2D-coordinate metrology system (e.g. mask placement inspection tools) or have 2D-metrology capability (e.g. electron-beam pattern generators and optical steppers). When using these apparatus, stage distortion typically manifests itself as a coordinate measurement error when measuring marks having known positions on a rigid artefact plate (“standard plate”).
The measurement of marks on a standard plate is a form of conventional calibration typically requiring two steps. The first step measures a standard plate having mark positions that are known to a higher degree of precision than the stage grid. The second step determines a mapping function (stage calibration function) between the measured coordinates and the actual coordinates, using a piece-wise linear function or polynomial fitting, as an approximation to the actual stage distortion.
Unfortunately, the use of standard plates to calibrate 2D metrology stages is no longer generally feasible because it is difficult to fabricate plates with mark positions at locations known with higher levels of accuracy than the levels obtainable with state-of-the-art metrology tools. To address this fundamental problem, self-calibration techniques have been developed to calibrate metrology stages using artefact plates with an array of mark positions having locations that are not precisely known. The only requirement is that the artefact plate is “rigid” so that the relative positions of the marks on the plate do not change when the plate is rotated or translated on the stage.
In U.S. Pat. No. 4,583,298 to Raugh, conventional self-calibration techniques are disclosed. Some conditions for achieving complete self-calibration were pointed out:
1) There must be at least three different measurement views including rotational displacement of the plate and a translational displacement (or another rotation about a different pivoting point) of the plate.
2) The pivoting points must be at different stage positions.
3) The lattice generated by the initial pivoting point pair must be dense.
However, the algorithm proposed was computationally expensive because it was non-linear and possible unstable in the presence of large random measurement noise.
An improved method for performing complete self-calibration of metrology stages was disclosed in U.S. Pat. No. 5,798,947 to Ye et al., by mapping each of a two-dimensional array of stage positions (u,v) to a corresponding position in a Cartesian coordinate grid (x,y) to determine the distortion there between. This mapping function is performed by a series of operations which use an orthogonal Fourier series to decouple the determination of a distortion function. A disadvantage with the method is that a rigid artefact plate having a two-dimensional N×N array of marks thereon, having a predetermined interval, has to be provided when making the measurements. Another disadvantage is that the rotation has to be ±90° and the translation has to be at least one interval.